Solving an exponential equation

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In summary, the conversation is about a student seeking help with a logarithmic function problem for their final exam. They are looking for help in converting the equation from exponential to logarithmic form.
  • #1
Sharpy1
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I'm doing some optional problems in preparation for my final in two weeks in one of my classes and I'm stumped on this one in particular

Express irrational solutions in exact form and as a decimal rounded to three decimal places.

Problem: 0.3(4^0.2x) = 0.2

I won't be able to look back here for a few days so some help within the next hour or so would be nice but not required thanks in advance for the help!
 
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  • #2
Re: Logarithmic Function Help Plz :(

I would begin by expressing the equation as follows:

\(\displaystyle 4^{\frac{x}{5}}=\frac{2}{3}\)

Now, given:

\(\displaystyle a^b=c\)

this implies:

\(\displaystyle \log_a(c)=b\)

So, how can you convert the above equation from exponential to logarithmic form?
 

FAQ: Solving an exponential equation

What is an exponential equation?

An exponential equation is an equation in which the variable appears in the exponent. It is typically written in the form y = ab^x, where a and b are constants and x is the variable.

How do you solve an exponential equation?

To solve an exponential equation, you can use logarithms. Take the logarithm of both sides of the equation, and then use the properties of logarithms to isolate the variable. You can also use trial and error or graphing to approximate the solution.

What are the common mistakes when solving an exponential equation?

One common mistake is forgetting to take the logarithm of both sides of the equation. Another mistake is misapplying the properties of logarithms. It's also important to check your solutions, as sometimes extraneous solutions can arise.

What is the difference between solving exponential equations with the same base and different bases?

When solving exponential equations with the same base, you can simply set the exponents equal to each other and solve for the variable. When solving exponential equations with different bases, you need to use logarithms to change the bases to be the same before you can set the exponents equal to each other.

What are the real-world applications of exponential equations?

Exponential equations can be used to model population growth, radioactive decay, and compound interest. They are also commonly used in fields such as finance, biology, and physics to analyze and predict various phenomena.

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